An imaginary economy has six distinct geographic regions; each has its own specific economic functions, as follows:
The regions also have the following annual requirements (all quantities measured in tons):
Using the national railroad, shipping costs are $1/ton per 100 miles for all hauls over 100 miles. Within 100 miles, all goods are carried by truck at a cost of $1.25/ton per 100 miles ($1/ton minimum charge). The distances (in miles) between regions are as follows:
Assume producing regions can meet all requirements, but that, due to government regulation, food production in sector A is restricted to half that of sector E.
Formulate a linear program that will meet the requirements and minimize the total transportation costs in the economy.